Competition in telecommunications market has been ongoing for just over a decade or since the state monopoly was abolished. A number of mobile telecommunications companies have been established after the state monopoly was abolished. Most of them are still in operation either as a standalone or via merger with other companies. In spite of the end of the monopoly in the telecommunications market competition has not been able to flourish on the basis of general rules of competition rather has the so-called sector, the specific regulation has been issued to ensure competition in this field. Monitoring the competition is very extensive and to this end there are two public organizations that do have the responsibility of monitoring the market. These are the Post and Telecom Administration of Iceland and the Bureau of Competition Authority which is responsible for measures to be taken against anti-competitive behaviour. In consideration of the institution of sector specific regulation it raised few questions, firstly if the Post and Telecom Administration employs another approach to market definition and significant market power than the Competition Authority. Secondly,, if the Competition Authority would exercise the general rules of the competition in a different way from what it would customarily exercise and thirdly what is sectors specific regulation part on the market and can the sector specific regulations prevent the abuse of marketing power? In this writing I will attempt to answer these questions thus clarify how the market and it’s monitoring works. Early findings are that there are no visible differences in the enforcement by the Competition Authority of the general rules of competition in the telecommunications as compared to other markets nor the methods of monitoring institutions. The establishment of Special Regulations to govern and maintain competition in the mobile communication market are considered beneficial. It is entirely possible to delay implementation for the time being, applying current competition regulations will suffice.